Conservative finite-volume forms of the Saint-Venant  equations for hydrology and urban drainage

Hodges, Ben R.

doi:https://doi.org/10.5194/hess-23-1281-2019

Articles | Volume 23, issue 3

https://doi.org/10.5194/hess-23-1281-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-23-1281-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 23, issue 3

Research article

| Highlight paper

|

07 Mar 2019

Research article | Highlight paper |

| 07 Mar 2019

Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage

Ben R. Hodges

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Final revised paper (published on 07 Mar 2019)
Preprint (discussion started on 25 Jun 2018)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'Review Comments', Anonymous Referee #1, 10 Sep 2018
- AC1: 'Response to Anonymous Reviewer 1', Ben Hodges, 28 Oct 2018
RC2: 'Review of "Conservative finite-volume forms..."', Anonymous Referee #2, 09 Nov 2018
- AC2: 'Response to Anonymous Reviewer 2', Ben Hodges, 18 Dec 2018

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Publish subject to revisions (further review by editor and referees) (03 Jan 2019) by Matthew Hipsey

AR by Ben Hodges on behalf of the Authors (04 Jan 2019) Author's response Manuscript

ED: Referee Nomination & Report Request started (07 Jan 2019) by Matthew Hipsey

RR by Anonymous Referee #2 (06 Feb 2019)

Suggestions for revision or reasons for rejection

I was very happy with the revised version of the manuscript, which is much more clear and easy to follow. I only have some minor comments, as reported below.
I thus suggest accepting the paper for publication in HESS.

Specific comments
-P. 1, l. 22: one “part” too many.
-page 3: I note that the free-surface elevation has been used in various 2D SVE models (e.g., Defina, 2000; Cea & Bladé, 2015; Viero, 2019), leading to well-balanced schemes without the need of including the bottom slope explicitly. As observed by Cea and Bladé (2015) and reported in Viero & Valipour (2017), a key strength of this approach is that the hydrostatic pressure gradient naturally balances the bed slope in the case of horizontal free surface. On the other hand, the resulting scheme is not suitable to deal with shock waves, for which a key aspect is the momentum balance between advective inertia and hydrostatic pressure. I leave it to the author to evaluate whether or not to add some comments on this point (it is not mandatory of course).
-p. 7, l. 3: maybe a “by” missing after “pioneered”?
-p. 7, l. 12: note that 1D channels has been treated using the Finite Element method also in the 1D-2D model by D’Alpaos & Defina (2007).
-p. 7, l. 14 and p. 35, l. 19: “Aricò” in place of “Arico”.
-p. 7, l. 22: also known as C-property.
-p.16, l.13: delete one “is”.
-p.20, l. 9: maybe “providing” rather than “provides”?
-Pag. 22, l. 23: Not a substantial question... I do not see that the term Te identically vanishes for a flat free surface. I see that, for a flat free surface, Te cancels out with the last two terms in the LHS of eq. (48).
-p. 27, l. 29: “to shift part”
-p. 28, l. 3: maybe
-p.31, eq. (74): u should not appear in the first member of this equation.
-p. 37, l.1: “Van Leer, B.”
-consider grouping some figures into multi-panel figures (e.g., Figs. 3 and 4, Figs. 5 and 6, Figs 7 and 8).

References
Cea, L., Bladé, E., 2015. A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications. Water Resour. Res. 51, 5464–5486. http://dx.doi.org/10.1002/2014WR016547.
D’Alpaos, L., Defina, A., 2007. Mathematical modeling of tidal hydrodynamics in shallow lagoons: a review of open issues and applications to the Venice Lagoon. Comput. Geosci. 33, 476–496. https://doi.org/10.1016/j.cageo.2006.07.009.
Defina, A., 2000. Two dimensional shallow flow equations for partially dry areas. Water Resour. Res. 36, 3251–3264. https://doi.org/10.1029/2000WR900167.
Viero, D.P., Valipour, M., 2017. Modeling anisotropy in free-surface overland and shallow inundation flows. Adv. Water Resour. 104, 1–14. https://doi.org/10.1016/j.advwatres.2017.03.007.
Viero, D.P., 2019. Modelling urban floods using a finite element staggered scheme with an anisotropic dual porosity model. J. Hydrol. 568, 247–259. https://doi.org/10.1016/j.jhydrol.2018.10.055.

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ED: Publish subject to technical corrections (19 Feb 2019) by Matthew Hipsey

AR by Ben Hodges on behalf of the Authors (19 Feb 2019) Author's response Manuscript

Short summary

A new derivation of the equations for one-dimensional open-channel flow in rivers and storm drainage systems has been developed. The new approach solves some long-standing problems for obtaining well-behaved solutions with conservation forms of the equations. This research was motivated by the need for highly accurate models of large-scale river networks and the storm drainage systems in megacities. Such models are difficult to create with existing equation forms.